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arXiv 0902.29962009-02-17math.STstat.TH

检测条件极值模型

Detecting a conditional extrme value model

Bikramjit Das, Sidney I. Resnick

备注：: 21 pages, 4 figures
DOI：: 10.1007/s10687-009-0097-3

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摘要：

在经典的极值理论中，极端事件的概率是假设随机向量的所有分量都在极值分布的一个吸引区域内来估计的。相比之下，条件极值模型假设多变量随机向量的分量的子集合上的吸引区域条件。该模型已在\cite{heffernan:tawn:2004,heffernan:resnick:2007,das:resnick:2008a}中进行了研究。在本文中，我们提出了三个统计作为工具来检测这个模型在一个二元设置。此外，建议的统计量也有助于区分两种形式的极限措施，在模型中获得。

英文摘要：

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes a domain of attraction condition on a sub-collection of the components of a multivariate random vector. This model has been studied in \cite{heffernan:tawn:2004,heffernan:resnick:2007,das:resnick:2008a}. In this paper we propose three statistics which act as tools to detect this model in a bivariate set-up. In addition, the proposed statistics also help to distinguish between two forms of the limit measure that is obtained in the model.

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